ALEX | Alabama Learning Exchange

Mathematics MA2015 (2016) Grade: 9-12 Algebra I	16 ) Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. [A-REI1]
Mathematics MA2015 (2016) Grade: 9-12 Algebra I	17 ) Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. [A-REI3] Alabama Alternate Achievement Standards AAS Standard: M.AAS.A.HS.17- Solve an equation of the form ax + b = c where a, b, and c are positive whole numbers and the solution, x, is a positive whole number to represent a real-world problem.
Mathematics MA2015 (2016) Grade: 9-12 Algebra II	4 ) Solve quadratic equations with real coefficients that have complex solutions. [N-CN7]
Mathematics MA2015 (2016) Grade: 9-12 Algebra II	21 ) Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [A-CED2]
Mathematics MA2015 (2016) Grade: 9-12 Algebra II	27 ) Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* [A-REI11]
Mathematics MA2015 (2016) Grade: 9-12 Algebra II with Trigonometry	4 ) Solve quadratic equations with real coefficients that have complex solutions. [N-CN7]
Mathematics MA2015 (2016) Grade: 9-12 Algebra II with Trigonometry	13 ) Use the structure of an expression to identify ways to rewrite it. [A-SSE2] Example: See x⁴ - y⁴ as (x²)² - (y²)², thus recognizing it as a difference of squares that can be factored as (x² - y²)(x² + y²).
Mathematics MA2015 (2016) Grade: 9-12 Algebra II with Trigonometry	21 ) Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [A-CED2]
Mathematics MA2015 (2016) Grade: 9-12 Algebra II with Trigonometry	27 ) Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* [A-REI11]
Mathematics MA2019 (2019) Grade: 7 Accelerated	24. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x). Limit to linear equations. [Algebra I with Probability, 19]
Mathematics MA2019 (2019) Grade: 9-12 Algebra I with Probability	5. Use the structure of an expression to identify ways to rewrite it. Example: See x⁴ - y⁴ as (x²)² - (y²)², thus recognizing it as a difference of squares that can be factored as (x² - y²)(x² + y²). Alabama Alternate Achievement Standards AAS Standard: M.A.AAS.11.5 Solve simple algebraic equations using real-world scenarios with one variable using multiplication or division.
Mathematics MA2019 (2019) Grade: 9-12 Algebra I with Probability	9. Select an appropriate method to solve a quadratic equation in one variable. a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)² = q that has the same solutions. Explain how the quadratic formula is derived from this form. b. Solve quadratic equations by inspection (such as x² = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation, and recognize that some solutions may not be real. Alabama Alternate Achievement Standards AAS Standard: M.A.AAS.11.9 Identify equivalent expressions given a linear expression using arithmetic operations.
Mathematics MA2019 (2019) Grade: 9-12 Algebra I with Probability	10. Select an appropriate method to solve a system of two linear equations in two variables. a. Solve a system of two equations in two variables by using linear combinations; contrast situations in which use of linear combinations is more efficient with those in which substitution is more efficient. b. Contrast solutions to a system of two linear equations in two variables produced by algebraic methods with graphical and tabular methods. Alabama Alternate Achievement Standards AAS Standard: M.A.AAS.11.9 Identify equivalent expressions given a linear expression using arithmetic operations.
Mathematics MA2019 (2019) Grade: 9-12 Algebra I with Probability	12. Create equations in two or more variables to represent relationships between quantities in context; graph equations on coordinate axes with labels and scales and use them to make predictions. Limit to contexts arising from linear, quadratic, exponential, absolute value, and linear piecewise functions. Alabama Alternate Achievement Standards AAS Standard: M.A.AAS.11.11 Select an equation or inequality involving one operation (limit to addition or subtraction) with one variable that represents a real-world problem. Solve the equation.
Mathematics MA2019 (2019) Grade: 9-12 Algebra I with Probability	14. Given a relation defined by an equation in two variables, identify the graph of the relation as the set of all its solutions plotted in the coordinate plane. Note: The graph of a relation often forms a curve (which could be a line). Alabama Alternate Achievement Standards AAS Standard: M.A.AAS.12.14 When given a relation in table form, identify the graph that represents the relation. (Ex: The points (5,5); (6,4); (3,7) are given to the student along with three graphs, and the student chooses the graph that represents the relation.)
Mathematics MA2019 (2019) Grade: 9-12 Algebra I with Probability	15. Define a function as a mapping from one set (called the domain) to another set (called the range) that assigns to each element of the domain exactly one element of the range. a. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Note: If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. b. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Limit to linear, quadratic, exponential, and absolute value functions. Alabama Alternate Achievement Standards AAS Standard: M.A.AAS.12.15 Use the vertical line test to determine if a given relation is a function.
Mathematics MA2019 (2019) Grade: 9-12 Algebra I with Probability	19. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x). a. Find the approximate solutions of an equation graphically, using tables of values, or finding successive approximations, using technology where appropriate. Note: Include cases where f(x) is a linear, quadratic, exponential, or absolute value function and g(x) is constant or linear. Alabama Alternate Achievement Standards AAS Standard: M.A.AAS.12.18 Interpret the meaning of a point on the graph of a line. (Ex.: On a graph of football ticket purchases, trace the graph to a point and tell the number of tickets purchased and the total cost.)
Mathematics MA2019 (2019) Grade: 9-12 Algebra I with Probability	20. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes, using technology where appropriate. Alabama Alternate Achievement Standards AAS Standard: M.A.AAS.12.18 Interpret the meaning of a point on the graph of a line. (Ex.: On a graph of football ticket purchases, trace the graph to a point and tell the number of tickets purchased and the total cost.)

How Many Solutions?: Algebra 1, Episode 14: Unit 7, Lesson 5 | Illustrative Math